Question: Multiply the following complex numbers: $({-3}) \cdot ({-2i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3}) \cdot ({-2i}) = $ $ ({-3} \cdot {0}) + ({-3} \cdot {-2}i) + ({0}i \cdot {0}) + ({0}i \cdot {-2}i) $ Then simplify the terms: $ (0) + (6i) + (0i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (6 + 0)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (6 + 0)i - 0 $ The result is simplified: $ (0 - 0) + (6i) = 6i $